Problem Sets 1 and 2 are now posted on
the Problem Sets page.
Course
Description
This course will investigate properties of some of the most common
moduli spaces in algebraic geometry -- moduli spaces of curves, moduli
spaces of vector bundles, Hilbert schemes and variants -- using
modern techniques -- schemes, sheaves, cohomology, intersection theory,
Grothendieck-Riemann-Roch, duality, positivity, and the Mori program.
The goal is both to see how modern techniques are applied to study
interesting varieties, but also to see how moduli spaces
themselves are a tool for studying questions in algebraic
geometry (and beyond).
Prerequisites
Students should have passed the graduate algebra sequence. A basic
understanding of the language of modern algebraic geometry will also
be essential.
Text
There is no required textbook. Our approach will be to survey
techniques with only a brief overview of proofs, but with links to the
literature. The list of references will grow as the semester progresses.
-
Harris, J. and Morrison, I. Moduli of curves.
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Huybrechts, D. and Lehn, M. Moduli of sheaves.
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A. J. de Jong and others, The Stacks Project.
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Mumford, D., Geometric invariant theory.
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Knutson, D., Algebraic spaces.
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Artin, M., Grothendieck topologies.
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Laumon, G., and Moret-Bailly, L., Champs algebriques.
-
Olsson, M., Algebraic stacks.
Lectures
The instructor for this course is
Jason Starr.
All instruction will occur in lectures. A tentative schedule will be posted
in the syllabus.
Lecture is held Tuesdays and Thursdays, 11 AM — 12:20PM in
Physics P—124.
Office Hours
Here is
a link
to the current office hours.
Grading System
As discussed at the first class meeting, grading will be based on
class participation.
If you have a physical, psychological, medical, or learning disability
that may impact your course work, please contact the Student
Accessibility Support Center, Stony Brook Union Suite 107, (631)
632-6748 or at sasc@Stonybrook.edu. They will determine with you what
accommodations are necessary and appropriate. All information and
documentation is confidential.
Student Accessibility Support Center
Students who require assistance during emergency evacuation are
encouraged to discuss their needs with their professors and SASC. For
procedures and information go to the following website:
Evacuation guide for people with physical disablilities
Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing another
person's work as your own is always wrong. Faculty is required to
report any suspected instance of academic dishonesty to the Academic
Judiciary. For more comprehensive information on academic integrity,
including categories of academic dishonesty, please refer to the
academic judiciary website at
Academic
Judiciary
Stony Brook University expects students to respect the rights,
privileges, and property of other people. Faculty are required to
report to the Office of Judicial Affairs any disruptive behavior that
interrupts their ability to teach, compromises the safety of the
learning environment, or inhibits students' ability to learn.
Further information about most academic matters can be found in the
Undergraduate Bulletin, the Undergraduate Class Schedule, and the
Faculty-Employee Handbook.
Back to my home page.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr
